We compare first order (refractive) ionospheric effects seen by the Murchison Widefield Array (MWA) with the ionosphere as inferred from Global Positioning System (GPS) data. The first order ionosphere manifests itself as a bulk position shift of the observed sources across an MWA field of view. These effects can be computed from global ionosphere maps provided by GPS analysis centres, namely the Center for Orbit Determination in Europe (CODE), using data from globally distributed GPS receivers. However, for the more accurate local ionosphere estimates required for precision radio astronomy applications, data from local GPS networks needs to be incorporated into ionospheric modelling. For GPS observations, the ionospheric parameters are biased by GPS receiver instrument delays, among other effects, also known as receiver Differential Code Biases (DCBs). The receiver DCBs need to be estimated for any non-CODE GPS station used for ionosphere modelling, a requirement for establishing dense GPS networks in arbitrary locations in the vicinity of the MWA. In this work, single GPS station-based ionospheric modelling is performed at a time resolution of 10 minutes. Also the receiver DCBs are estimated for selected Geoscience Australia (GA) GPS receivers, located at Murchison Radio Observatory (MRO1), Yarragadee (YAR3), Mount Magnet (MTMA) and Wiluna (WILU). The ionospheric gradients estimated from GPS are compared with the ionospheric gradients inferred from radio source position shifts observed with the MWA. The ionospheric gradients at all the GPS stations show a correlation with the gradients observed with the MWA. The ionosphere estimates obtained using GPS measurements show promise in terms of providing calibration information for the MWA.